Karen takes 4 hours less than Foggy to complete a task.

Question

Karen takes 4 hours less than Foggy to complete a task. Working together, they could complete 62.5% of the task in 3 hours. In how many hours can Foggy, working alone, complete 50% of the task?

(A) 3
(B) 6
(C) 8
(D) 9
(E) 12

Ashu9876 · Accepted Answer

62.5% of work can be done in 3hours 
Then, 
100% of work can be done in = 3×100/62.5=24/5 hours 
If time taken by Foggy to complete 50% of job – x 
Time taken by Foggy to complete 100% of job – 2x 
Time taken by Karen to complete 100% of work – 2x- 4
1/2x+1/(2x-4)=5/24 
Using the Answer choices, 
(A) 3
(B) 6 – 1/12+1/8=20/96=5/24
(C) 8
(D) 9
(E) 12
Hence, Answer is B

gmatophobia · Answer

The crux of solving such questions is to get the units at an equal level. For. example, we are given the time both Foggy and Karen take to complete 62.5% of the task. It's much easier to deal with questions when we know the time both will take to complete 100% of the task

Let's first find that out -

To complete 62.5 % of the task both take 3 hours.

To complete 100% of the task they will take  \frac{3}{62.5} * 100  =  \frac{30 * 100}{625} = \frac{24}{5 }  hours.

Now, the question wants us to find "In how many hours can Foggy, working alone, complete  50%  of the task". Let's use the options here. So if Foggy takes x hours to do 50% of the work, he/she will take twice the amount of time to do 100% of the work.

Let's move all the options to reflect 100% work instead of 50% of work-

(A) 6
(B) 12
(C) 16
(D) 18
(E) 24

We also know that Karen takes 4 hours less than Foggy to complete a task. As the option now tells us how much time Foggy takes to complete 100% of the work, we can find the time Karen will take to complete 100% of the same work -

Also, from our earlier calculations, we found out that both of them take  \frac{24}{5}  hours to complete 100% of the same job.

If person "A" takes time  t_1  to complete a job and person "B" takes time  t_2  to complete the same job, the time taken together can be found out by -

\frac{t_1 * t_2 }{ t_1 + t_2}

Let's use the options to out advantage here and see which option matches the total time -

(A) Foggy: 6 | Karen : 2

Together ⇒  \frac{12 }{ 8}  --  OUT

(B) Foggy: 12 | Karen : 8

Together ⇒  \frac{12*8 }{ 20}  =  \frac{24 }{ 5}  --  BINGO!

We can stop here and Option B is the right answer.

(C) Foggy: 16 | Karen : 12
(D) Foggy: 18 | Karen : 14
(E) Foggy : 24 | Karen: 20

Option B

KarishmaB · Answer

Time taken by Foggy = F hrs
Time taken by Karen = F - 4 hrs

Working together they complete 62.5% i.e. 5/8th of the work in 3 hrs. So they complete 5/24th of the work every hour.

\frac{1}{F} + \frac{1}{F-4} = \frac{5}{24}

The options give us time taken by Foggy for half the work. So twice the options represent F. (6 or 12 or 16 or 18 or 24)
Trick in this question is to get the value of F. We may not want to try every option since that could be time consuming. Note that we have 24 as the denominator on the right hand side. So we are looking for a 3 and three 2s. 
If F is 6, F - 4 is 2 so we do not get three 2s.
If F is 12, F - 4 is 8 so we DO get a 3 and three 2s. This is the first option we should try. We find that it works. 
If F is 16, we would have four 2s so we will ignore it.
If F is 18, we would have two 3s so we will ignore it.
If F is 24, F - 4 = 20 which would give us a 5 as a factor too. Ignore.

Using the denominator of RHS, try to find the option with similar factors to try first to hasten the process.

Answer (B)

Dream009 · Answer

I assumed foggy's rate as 4x and Karen's as 4x-4
1/4x + 1/4x-4 = 24
2x-1/(x)(x-1) = 5/6
=> x = 3
4x= 12 - Answer in 1 min

Dream009 · Answer

I assumed foggy's rate as 4x and Karen's as 4x-4
1/4x + 1/4x-4 = 24
2x-1/(x)(x-1) = 5/6
=> x = 3
4x= 12 - Answer in 1 min

Wadree · Answer

Ts calls for OPTION CHECK.......
Option 1....
if foggy does 50% in 3 hrs... He does 100% in 6 hrs...so karen will do 100% in 6 - 4 = 2 hrs....
So...in 3 hrs ... They'll together do =   + 50 = 200% ... but they should complete only 62.5% together in 3 hrs....
Option 2....
if foggy does 50% in 6 hrs... He does 100% in 12 hrs...so karen will do 100% in 12 - 4 = 8 hrs....
So...in 3 hrs ... They'll together do =   +   = 62.5 % ....
So checks out..... LESSS GOOOO........

pappal · Answer

let foggy takes f hrs so Karen takes (f-4) hrs
combined rate =1/f + 1/(f-4)=2f-4 / f(f-4)---------1
62.5% of work is completed in 3 hrs 
so 100% work is completed in 3*100 / 62.5=25/5=4.8 hrs ---------2
on multiplying rate in 1 and the time in 2, work completed is 100% or '1'
solving {1/f + 1/(f-4)}*4.8=1
we get f=12 or f=8/5(discard this value since time for Karen f-4 cant be negative)
if f=12 hrs for 100% work
so time for Karen to complete 50% WORK=6 hrs
so B

Karen takes 4 hours less than Foggy to complete a task.

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